Background. Hardware, software, and people are often tested in one set of conditions, but are expected to perform under many different circumstances. For example, consider pedestrian headform testing. An approximate sphere, with an accelerometer inside it, is projected at the front of a car. The speed is specified, but real pedestrian impacts are at a wide range of speeds. The headform mass is specified, but real pedestrians have a range of effective head masses. The acceleration trace is summarised in order to check that the car is not overly injurious if a pedestrian is struck. This paper will set out the principles of calculating the real-world consequences --- that is, averaged over the range of speeds and effective head masses --- of a particular test result under specified test conditions. Such a calculation is not common in the road safety world, and we do not think it is common in other testing contexts. It is a specific example of the more general problem of using performance in particular test conditions to estimate average real-world performance. (But note that the discussion is not primarily about going from one condition to another, such as from harsh conditions in which failure is accelerated to normal conditions in which failure is infrequent. At least in our context, the test conditions are realistic. The issue is rather that of averaging over a variety of conditions.) Proposed procedure. It is proposed to calculate an estimate of the average level of performance --- averaged over different conditions, that is. This calculation has three components. (1) An equation for the dependence of performance on conditions. (2) An equation for the cost of (i.e., how bad or good are) different levels of performance. (3) The probabilities of different conditions. The three components come together in a summation or integration that represents the averaging over different impact conditions. Applications. The equation permits, for example, the calculation of the changes that result if test performance is improved, or the probabilities of different conditions change. This paper will present the specific methods we have developed, and will suggest they can be expressed in quite general language. Our interest is in impact testing, but the core issue --- the implications for average real-world performance of a test in one set of conditions --- must be in the minds of people concerned with a great variety of tests.
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